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Aren't the same conditions true for chess, though there is no proof that a best strategy exists?

What if it's not just rock/paper/scissors, and there are more than 3 strategies?

There is no fundamental difference between Chess and Tic-Tac-Toe other than the computational complexity. It is not feasible to compute all of the game states in Chess, and so we cannot determine (at this time) a single optimal strategy the same way we can for Tic-Tac-Toe. But that does not imply that it doesn't exist. From a pure game theoretical perspective, they are the same category of game.

If there are more than 3 strategies, the same argument stands. IF there are multiple "optimal" strategies, AND these strategies create different "optimal" moves on the same board state, the opponent can just play the optimal counter-strategy after you make your move, because your move is enough information to give away your strategy. If your opponent cannot determine your strategy after you make your move, that implies the different strategies have the same "optimal" move.

At least one of the players has a strategy that cannot be countered though. That is, either white can force a win, black can force a win, or both players can force a draw. There is no situation where every strategy can be countered.

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